I am asked to find a defining set of a binary cyclic code of length 15 which isn't a BCH code.
I already found the 2-cyclotomic cosets:
$C_0 = \{0\}$, $C_1 = \{1,2,4,8\}$, $C_3 = \{3,6,9,12\}$, $C_5 = \{5,10\}$, $C_7 = \{7,11,13,14\}$
but I am not sure how to get a definig set of a binary cyclic code of length 15. How can I find the defining set?